In my viewport, some faces look like they are either disconnected from the rest of my mesh by means of duplicate vertices or edges, or they look like their normals are opposite to the rest of the mesh.
But the tools for fixing these problems fail to find such problems. According to these tools, there's no duplicates to merge, and the normals ARE consistent.
What other strange geometry problems could make my faces look inconsistent in my viewport?
Added a share of my file as requested: